A Riemann–Hilbert approach was used to discuss matrix biorthogonal polynomials of Hermite [1]}, [2]}, [3]}, [4]} and Laguerre type [5]}.
In this paper, we focus on Jacobi type examples:
We say that a matrix of weights \(W=\begin{bsmallmatrix}W^{(1,1)} & \cdots & W^{(1,N)} \\\vdots & \ddots & \vdots \\W^{(N,1)} & \cdots & W^{(N,N)}\end{bsmallmatrix}\in { N\times N}\)  with support \(\gamma \)  is of Jacobi type if
the entries \(W^{(j, k)}\)  of the matrix measure \(W\)  can be written as
\(W^{(j, k)}(z)=\sum _{m \in I_{j, k}} \varphi _{m}(z) (a+z)^{\alpha _{m}}(b-z)^{\beta _m} \log ^{p_{m}} (a+z)\log ^{q_m}(b-z),&&z \in \gamma ,\) 
